Theorem tpcomb 4723

Description: Swap 2nd and 3rd members of an unordered triple. (Contributed by NM, 22-May-2015.)

Assertion

Ref	Expression
tpcomb	⊢ {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}

Proof of Theorem tpcomb

Step	Hyp	Ref	Expression
1		tpcoma 4722	. 2 ⊢ {𝐵, 𝐶, 𝐴} = {𝐶, 𝐵, 𝐴}
2		tprot 4721	. 2 ⊢ {𝐴, 𝐵, 𝐶} = {𝐵, 𝐶, 𝐴}
3		tprot 4721	. 2 ⊢ {𝐴, 𝐶, 𝐵} = {𝐶, 𝐵, 𝐴}
4	1, 2, 3	3eqtr4i 2763	1 ⊢ {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}

Syntax hints:   = wceq 1540  {ctp 4601

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3or 1087  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-v 3457  df-un 3927  df-sn 4598  df-pr 4600  df-tp 4602

This theorem is referenced by:  f13dfv  7256  frgr3v  30211  tpssad  32475  signswch  34560  signstfvcl  34572  dvh4dimN  41433